Share
Explore BrainMass

Combinatorial and Computational Number Theory

See attached file for full problem description.

(a) Prove that if g.c.d.(n,p) = 1,then p divides n^(p-1) -1.
(b) Prove that if 3 is not a divisor of n, then 3 divides n^2 -1.
(c) Prove that if 5 is not a divisor of (n - 1), 5 is not a divisor of n,and 5 is not a divisor of (n+1), then 5 divides (n^2 + 1).

Solution Summary

This solution is comprised of a detailed explanation for Combinatorial and Computational Number Theory.
It contains step-by-step explanation for finding the solution of the problems, that are
(a) Prove that if g.c.d.(n,p) = 1,then p divides n^(p-1) -1.
(b) Prove that if 3 is not a divisor of n, then 3 divides n^2 -1.
(c) Prove that if 5 is not a divisor of (n - 1), 5 is not a divisor of n,and 5 is not a divisor of (n+1), then 5 divides (n^2 + 1).

$2.19